86:@0.057273:0.966074:0.076087:0.966074:0.076087:0.949450:0.057273:0.949450:0.000000:0.000000
Olimpiadas matemáticas:@0.107368:0.074738:0.438969:0.074738:0.438969:0.046697:0.107368:0.046697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. :@0.096359:0.125354:0.115100:0.125354:0.115100:0.108218:0.096359:0.108218:0.000000:0.000000:0.000000
Observa:@0.124848:0.125354:0.191370:0.125354:0.191370:0.108454:0.124848:0.108454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la figura y :@0.191370:0.125354:0.270425:0.125354:0.270425:0.109684:0.191370:0.109684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
determina:@0.270425:0.125354:0.353310:0.125354:0.353310:0.108454:0.270425:0.108454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 el valor del área verde::@0.353310:0.125354:0.520484:0.125354:0.520484:0.109684:0.353310:0.109684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.516067:0.261320:0.519974:0.261320:0.519974:0.244696:0.516067:0.244696:0.000000
Argumenta:@0.538033:0.261320:0.628531:0.261320:0.628531:0.244419:0.538033:0.244419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.628531:0.261320:0.632253:0.261320:0.632253:0.244184:0.628531:0.244184:0.000000
la solución.:@0.631719:0.261320:0.712764:0.261320:0.712764:0.245650:0.631719:0.245650:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.516067:0.451998:0.519974:0.451998:0.519974:0.435374:0.516067:0.435374:0.000000
Argumenta:@0.538033:0.451998:0.628531:0.451998:0.628531:0.435098:0.538033:0.435098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.628531:0.451998:0.632253:0.451998:0.632253:0.434863:0.628531:0.434863:0.000000
la solución.:@0.631719:0.451998:0.712764:0.451998:0.712764:0.436329:0.631719:0.436329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.097428:0.551411:0.101335:0.551411:0.101335:0.534787:0.097428:0.534787:0.000000
Argumenta:@0.125917:0.551411:0.216415:0.551411:0.216415:0.534510:0.125917:0.534510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.216415:0.551411:0.220138:0.551411:0.220138:0.534275:0.216415:0.534275:0.000000
la solución.:@0.219603:0.551411:0.300648:0.551411:0.300648:0.535741:0.219603:0.535741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.350071:0.895979:0.353977:0.895979:0.353977:0.879355:0.350071:0.879355:0.000000
Argumenta:@0.378560:0.895979:0.469056:0.895979:0.469056:0.879078:0.378560:0.879078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.469056:0.895979:0.472779:0.895979:0.472779:0.878843:0.469056:0.878843:0.000000
la solución.:@0.472688:0.895979:0.554212:0.895979:0.554212:0.880309:0.472688:0.880309:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.096967:0.647407:0.100874:0.647407:0.100874:0.630783:0.096967:0.630783:0.000000
Argumenta:@0.125456:0.647407:0.215953:0.647407:0.215953:0.630506:0.125456:0.630506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.215953:0.647407:0.219675:0.647407:0.219675:0.630271:0.215953:0.630271:0.000000
la solución.:@0.219585:0.647407:0.301109:0.647407:0.301109:0.631737:0.219585:0.631737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.096967:0.725355:0.100874:0.725355:0.100874:0.708731:0.096967:0.708731:0.000000
Argumenta:@0.125456:0.725355:0.215953:0.725355:0.215953:0.708454:0.125456:0.708454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.215953:0.725355:0.219675:0.725355:0.219675:0.708219:0.215953:0.708219:0.000000
la solución.:@0.219585:0.725355:0.301109:0.725355:0.301109:0.709685:0.219585:0.709685:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2. :@0.096359:0.310570:0.115100:0.310570:0.115100:0.293434:0.096359:0.293434:0.000000:0.000000:0.000000
El cuadrado ABCD tiene lados de longitud de 6 cm. Los puntos M y N están sobre AD y AB, respectivamente, :@0.124848:0.310570:0.907581:0.310570:0.907581:0.294900:0.124848:0.294900:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de forma que CN y CM dividen el cuadrado en tres regiones de la misma área. ¿Cuál es la longitud de NB? :@0.124848:0.327166:0.898617:0.327166:0.898617:0.311496:0.124848:0.311496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3. :@0.096359:0.496408:0.115100:0.496408:0.115100:0.479272:0.096359:0.479272:0.000000:0.000000:0.000000
Cristina está practicando el salto de longitud. El promedio de las distancias que saltó en los primeros inten-:@0.124848:0.496408:0.903727:0.496408:0.903727:0.480738:0.124848:0.480738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tos de hoy es 3,80 m. En su siguiente intento, saltó 3,99 m y su promedio alcanzó los 3,81 m. ¿Qué distancia :@0.124848:0.513004:0.907816:0.513004:0.907816:0.497334:0.124848:0.497334:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
debe alcanzar en su próximo salto para aumentar su promedio a 3,82 m?:@0.124848:0.529600:0.657160:0.529600:0.657160:0.513931:0.124848:0.513931:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4. :@0.096359:0.585848:0.115100:0.585848:0.115100:0.568712:0.096359:0.568712:0.000000:0.000000:0.000000
En un torneo, la mitad de los competidores se eliminan en cada ronda (si al principio de la ronda el número :@0.124848:0.585848:0.907783:0.585848:0.907783:0.570178:0.124848:0.570178:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de competidores es impar, uno de ellos se selecciona al azar y se queda para la siguiente ronda). Si empie-:@0.124848:0.602445:0.903637:0.602445:0.903637:0.586775:0.124848:0.586775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
zan 100 competidores, ¿cuántas rondas deben pasar para que quede un ganador final?:@0.124848:0.619041:0.761483:0.619041:0.761483:0.603371:0.124848:0.603371:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5. :@0.096359:0.681416:0.115100:0.681416:0.115100:0.664280:0.096359:0.664280:0.000000:0.000000:0.000000
¿De cuántas formas puedo elegir 7 números del 1 al 9 de manera que al sumarlos el resultado sea un múl-:@0.124848:0.681416:0.903580:0.681416:0.903580:0.665746:0.124848:0.665746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tiplo de 3?:@0.124848:0.698012:0.201323:0.698012:0.201323:0.682342:0.124848:0.682342:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
6. :@0.096359:0.757054:0.115100:0.757054:0.115100:0.739918:0.096359:0.739918:0.000000:0.000000:0.000000
¿Cuánto vale   en la siguiente figura?:@0.124848:0.757054:0.395235:0.757054:0.395235:0.741384:0.124848:0.741384:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.223270:0.757054:0.230733:0.757054:0.230733:0.740692:0.223270:0.740692:0.000000
24 cm:@0.217611:0.157830:0.258822:0.157830:0.258822:0.143585:0.217611:0.143585:0.000000:0.000000:0.000000:0.000000:0.000000
16 cm:@0.353306:0.198064:0.394516:0.198064:0.394516:0.183819:0.353306:0.183819:0.000000:0.000000:0.000000:0.000000:0.000000
10 cm:@0.433717:0.239555:0.474928:0.239555:0.474928:0.225310:0.433717:0.225310:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.241768:0.457910:0.251568:0.457910:0.251568:0.443665:0.241768:0.443665:0.000000
D:@0.241249:0.362519:0.252088:0.362519:0.252088:0.348274:0.241249:0.348274:0.000000
M:@0.240143:0.421926:0.253176:0.421926:0.253176:0.407681:0.240143:0.407681:0.000000
B:@0.390797:0.457910:0.399257:0.457910:0.399257:0.443665:0.390797:0.443665:0.000000
N:@0.304154:0.465027:0.314842:0.465027:0.314842:0.450781:0.304154:0.450781:0.000000
C:@0.390261:0.362531:0.399810:0.362531:0.399810:0.348286:0.390261:0.348286:0.000000
Recuperado de: http://www.ommenlinea.org/:@0.657678:0.945082:0.903640:0.945082:0.903640:0.933686:0.657678:0.933686:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
81 cm:@0.178617:0.877586:0.219827:0.877586:0.219827:0.863341:0.178617:0.863341:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.219826:0.872088:0.224592:0.872088:0.224592:0.863784:0.219826:0.863784:0.000000
x:@0.219179:0.782754:0.225964:0.782754:0.225964:0.767880:0.219179:0.767880:0.000000
x:@0.321369:0.861964:0.328153:0.861964:0.328153:0.847090:0.321369:0.847090:0.000000
18 cm:@0.283569:0.886982:0.283569:0.856052:0.264588:0.856052:0.264588:0.886982:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.276244:0.856052:0.276244:0.852475:0.265178:0.852475:0.265178:0.856052:0.000000
332 cm .:@0.539860:0.277099:0.579806:0.277099:0.579806:0.267127:0.539860:0.267127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.574429:0.273251:0.577765:0.273251:0.577765:0.267437:0.574429:0.267437:0.000000
NB mide 4 cm.:@0.545154:0.461104:0.612981:0.461104:0.612981:0.451132:0.545154:0.451132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Debe alcanzar 4,01 en su salto siguiente.:@0.333839:0.550153:0.521685:0.550153:0.521685:0.540182:0.333839:0.540182:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
7:@0.390796:0.643269:0.396518:0.643269:0.396518:0.633297:0.390796:0.633297:0.000000
12:@0.332725:0.721229:0.344170:0.721229:0.344170:0.711258:0.332725:0.711258:0.000000:0.000000
11:@0.378764:0.917388:0.390209:0.917388:0.390209:0.907417:0.378764:0.907417:0.000000:0.000000